When DD (now 18mo) was smaller I fed her to sleep every time. She gradually began taking more cow's milk during the day and at 13mo I stopped feeding her. I was 'lucky' though as she would take a dummy, and so I would cuddle her at night with the dummy in and she would fall asleep pretty quickly.
By about 15mo I decided I had to crack the going to sleep on her own thing. We used PUPD, so I would do the bedtime routine, bath, story, light out, quick cuddle then lie her in her cot and say 'Night night, love you.' She would scream, so I picked her up, cuddled till calm, then put her back down, and repeat the phrase. Eventually she was calm enough to stay in the cot and I would pat her back rhythmically till she fell asleep. I gradually tried leacing the room before she was quite asleep, but would go straight back in if she yelled.
After about 4 or 5 weeks of this, I put her down, said 'Night night, love you' and left the room. She went straight to sleep. Now, she generally goes to sleep that quickly - it's only when she's poorly or there are fireworks 
that she doesn't settle quickly.
I think I knew at the start that it wouldn't be a quick fix, but that with consistency we'd get there in the end and we have. Unfortunately, she still doesn't reliably sleep through the night, but we're getting there. Occasionally she will yell when I put her down and walk out of the room, but I wait for a little, and usually within 30 seconds she's gone quiet, even if she was full-on screaming! I guess it's a matter of learning when you need to go back in and when you don't.